Generalized theory of diffraction tomography for random media

The theory of diffraction tomography is generalized to random media. A relationship between the two-point spatial correlation function of the dielectric susceptibility and the cross-spectral density of the scattered field is derived, and the reconstruction of the two-point spatial correlation function from measurements of the cross-spectral density in two planes, on different sides and at finite distances from the medium, is investigated. It is shown that the two-point spatial correlation function cannot be determined uniquely, in general, from scattered field measurements, except for a class of random media known as quasi-homogeneous random media.